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Additional info for MATLAB The Language of Technical Computing (Mathematics) ~ Version 7
Sample text
This is the default method for the interp1 function. • Cubic spline interpolation (method = 'spline'). This method fits a different cubic function between each pair of existing data points, and uses the spline function to perform cubic spline interpolation at the data points. • Cubic interpolation (method = 'pchip' or 'cubic'). These methods are identical. They use the pchip function to perform piecewise cubic Hermite interpolation within the vectors x and y. These methods preserve monotonicity and the shape of the data.
When A does not have full rank, the triangular structure of R makes it possible to find a basic solution to the least squares problem. 1-34 Matrix Powers and Exponentials Matrix Powers and Exponentials This section tells you how to obtain the following matrix powers and exponentials in MATLAB: • Positive integer • Inverse and fractional • Element-by-element • Exponentials Positive Integer Powers If A is a square matrix and p is a positive integer, then A^p effectively multiplies A by itself p-1 times.
If b = A(:,2) is the second column, then an obvious solution to A*x = b is x = [0 1 0]'. But none of the approaches computes that x. The backslash operator gives x = A\b Warning: Rank deficient, rank = 2. 5000 This solution has two nonzero components. 3333 1-26 Inverses and Determinants There is no warning about rank deficiency. 7071. Finally z = inv(A'*A)*A'*b fails completely. Warning: Matrix is singular to working precision. z = Inf Inf Inf 1-27 1 Matrices and Linear Algebra Cholesky, LU, and QR Factorizations The MATLAB linear equation capabilities are based on three basic matrix factorizations: • Cholesky factorization for symmetric, positive definite matrices • LU factorization (Gaussian elimination) for general square matrices • QR (orthogonal) for rectangular matrices These three factorizations are available through the chol, lu, and qr functions.
MATLAB The Language of Technical Computing (Mathematics) ~ Version 7 by The MathWorks
by Charles
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